Linking anisotropic sharp and diffuse surface motion laws via gradient flows
type: Item
instance of: scholarly article
title: Linking anisotropic sharp and diffuse surface motion laws via gradient flows
zbMATH Open document ID: 0844.35044
DOI: 10.1007/BF02186838
author: J. W. Cahn
author: Jean E. Taylor
published in: Journal of Statistical Physics
publication date: 1996-03-19T00:00:00Z
review text: The authors consider four laws of motion for sharp surfaces (e.g., motion by mean curvature or by the negative Laplacian of the mean curvature) and show that they can all be interpreted as gradient flows of the same energy functional corresponding to different choices of inner product. Anisotropic as well as isotropic energies are considered. They also obtain analogous results for the diffuse interface counterparts of these equations (e.g., Allen-Cahn and Cahn-Hilliard equations). For both classes of examples the anisotropy of the kinetics is incorporated into the inner product, not into the energy functional.
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 82C24
zbMATH DE Number: 843815
zbMATH Keywords: Allen-Cahn equation
zbMATH Keywords: diffuse interfaces
zbMATH Keywords: anisotropy
zbMATH Keywords: motion for sharp surfaces
zbMATH Keywords: motion by mean curvature
zbMATH Keywords: Cahn-Hilliard equations
reviewed by: John Urbas
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02186838
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description: scientific article; zbMATH DE number 843815